Description
Present two different types of data, or variables, used in the health field. Examples could be blood pressure, temperature, pH, pain rating scales, pulse oximetry, % hematocrit, minute respiration, gender, age, ethnicity, etc.
Classify each of your variables as qualitative or quantitative and explain why they fall into the category that you chose.
Also, classify each of the variables as to their level of measurement–nominal, ordinal, interval or ratio–and justify your classifications.
Which type of sampling could you use to gather your data? (stratified, cluster, systematic, and convenience sampling)
Minimum of 1 scholarly source AND one appropriate resource such as the textbook, math video and/or math website
In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s).
This week we learned all about data. Think about a research study or question you may be interested in answering and explain what variables you might need to collect to answer your question. Describe and categorize those variables, and explain how you would collect your data. Provide a population of interest and how you could sample from that population.
You may also want to consider the difficulties or problems you may run into when trying to gather your data. Remember the big idea in statistics is to take a representative sample from a large population and be able to make inferences from your sample data about the whole population! However, this is not always easy as Stopher (2012) points out, “Survey sampling methodology can be defined as the science of choosing a sample that provides an acceptable compromise between sample cost and sample representativeness.”
Stopher, P. (2012). Collecting, managing, and assessing data using sample surveys. Cambridge University Press.
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Sampling Data: An Overview of
Statistics
An Overview of Statistics
Vocabulary:
•
Data: Consist of information coming from observations, counts,
measurements, or responses.
•
Statistics: The science of collecting, organizing, analyzing, and interpreting
data in order to make decisions.
•
Population: The collection of all outcomes, responses, measurements, or
counts that are of interest.
•
Sample: A subset of the population.
•
Parameter: A number that describes a population characteristic.
•
Statistic: A number that describes a sample characteristic.
•
Descriptive Statistics: Involves organizing, summarizing, and displaying
data. e.g. Tables, charts, averages
•
Inferential Statistics: Involves using sample data to draw conclusions
about a population.
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Example: Determine whether the data set is a population or a sample. Explain your
reasoning.
The salary of each teacher in a school.
a) Population, because it is a collection of salaries for all teachers in the school.
b) Sample, because it is a collection of salaries for some teachers in the school.
c) Population, because it is a subset of all schools in the city.
d) Sample, because it is a collection of salaries for all teachers in the school but
there are other schools.
The grade of 5 students in a classroom of 30.
a) Sample, because it is a collection of grades for all students in the classroom,
but there are other classrooms.
b) Population, because it is a collection of grades for all students in the
classroom.
c) Sample, because the collection of 5 students’ grades is a subset of all students
in the class.
d) Population, because it is a subset of all students in the class.
Example: In a poll, 1001 adults in a country were asked whether they favor or
oppose the use of “federal tax dollars to fund medical research using stem cells
obtained from human embryos.” Among the respondents, 48% said that they were
in favor. Describe the statistical study.
What is the population in the given problem?
a) The 1001 adults selected.
b) 48% of the 1001 adults selected.
c) 48% of the adults in the country
d) All adults in the country.
Identify the sample for the given problem.
a) The 1001 adults selected.
b) 48% of the 1001 adults selected.
c) 48% of the adults in the country
d) All adults in the country.
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Example: Determine whether the given value is a statistic or a parameter.
A sample of seniors is selected and it is found that 65% own a television.
a) Statistic because the value is a numerical measurement describing a
characteristic of a population.
b) Statistic because the value is a numerical measurement describing a
characteristic of a sample.
c) Parameter because the value is a numerical measurement describing a
characteristic of a population.
d) Parameter because the value is a numerical measurement describing a
characteristic of a sample.
In a study of all 4272 employees at a college, it is found that 65% own a
computer.
a) Statistic because the value is a numerical measurement describing a
characteristic of a population.
b) Statistic because the value is a numerical measurement describing a
characteristic of a sample.
c) Parameter because the value is a numerical measurement describing a
characteristic of a population.
d) Parameter because the value is a numerical measurement describing a
characteristic of a sample.
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Data Classification
Vocabulary
•
Qualitative Data: Consists of attributes, labels, or nonnumerical entries.
•
Quantitative Data: Numerical measurements or counts.
Example: Determine whether the variable is qualitative or quantitative.
a) Number of flights leaving an airport each year.
______________________________________
b) Favorite Sport. ___________________________________________
c) Age. ___________________________________________
d) Telephone Number. _____________________________________________
e) Social Security Number. ________________________________________________
Levels of Measurement
Level of
Measurement
Nominal
Definition
•
•
•
Ordinal
•
•
•
Interval
•
•
•
•
Example
Qualitative ONLY
Uses Names, Labels, or Qualities
NO MATH computations can be made at
this level.
Qualitative or Quantitative
Arranged in order or ranked
Differences between data are not
meaningful
Networks in Killeen, TX
Quantitative Data ONLY
Can be ordered
MEANINGFUL differences between data
can be calculated.
Not an Inherent Zero—Zero is just a
position on a scale
NY Yankees World Series Victories
(Years)
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ABC, NBC, CBS, FOX
Top 5 Football Teams
1. Seahawks
2. Broncos
3. Panthers
4. Saints
5. 49ers
As of 12/29/13
1923, 1927, 1928, 1932, …
Ratio
•
•
•
•
Quantitative Data ONLY
Can be ordered
MEANINGFUL differences between data
can be calculated.
Inherent Zero—Zero means none, an
absence of value.
Homerun Totals in 2009
Texas 224
Boston 212
Baltimore 160
Cleveland 161…
Example: The masses (in grams) of a sample of a species of fish caught in the water
of a region are shown below.
22.8
25.7
22.1
23.6
27.2
24.3
Determine whether the data are qualitative or quantitative and identify the level of
measurement.
Example:
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Example: Determine whether the following examples are Nominal, Ordinal,
Interval or Ratio.
1. Lengths of songs on an MP3 player
2. Wait times at an amusement park
3. The three political parties in the 111th Congress: Republican, Democrat,
Independent
4. Number of years at a job
5. The top five hardcover nonfiction books on the New York Times Best Seller List
of 2010:
1. Committed
2. Have a Little Faith
3. The Checklist Manifesto 4. Going Rogue
5. Stones Into Schools
6. Telephone numbers in a phone book
7. Year of birth
8. Daily temperatures in Colorado
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Discrete vs. Continuous Data
A random variable is __________________________ if it has a finite or countable number of
possible outcomes that can be listed.
A random variable is _________________________ if it has an uncountable number of
possible outcomes, represented by an interval on the number line.
Example: Decide whether the random variable “x” is discrete or continuous.
a) “x” represents number quarters needed in a parking meter.
b) “x” represents the height above the ground when skydiving.
c) “x” represents the time needed when taking an exam.
d) “x” represents the number of movie tickets needed for a family to see the
movies.
Given a Table—
Independent/Explanatory Dependent/Response
Variable (x)
Variable (y)
ON THE LEFT
ON THE RIGHT
Independent/Explanatory ON TOP
Variable (x)
Dependent/Response
ON
Variable (y)
BOTTOM
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Data Collection and Experimental Design
Designing a Statistical Study
1. Identify the variable(s) of interest (the focus) and the population of the study.
2. Develop a detailed plan for collecting data. If you use a sample, make sure the
sample is representative of the population.
3. Collect the data.
4. Describe the data, using descriptive statistics techniques.
5. Interpret the data and make decisions about the population using inferential
statistics.
6. Identify any possible errors.
Example: A candy manufacturer is interested in the distribution of colors in each of
its packages of candy sold. What should researchers do first?
A. Write a question about the distribution of colors in each package.
B. Choose a random sample of candy packages to analyze.
C. Make some initial conclusions about the distribution of the colors.
D. Make some initial conclusions about colors most people want.
Data Collection: Types of Studies
1. Observational Studies—You watch but you do not change existing
conditions.
Ex: __________________________________________________________________________
2. Experiment—a treatment is applied. Control Group: no treatment is
applied…maybe a placebo is given.
Ex: __________________________________________________________________________
3. Simulation: use of a mathematical or physical model to reproduce the
conditions of a situation or process.
Ex: __________________________________________________________________________
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4. Survey: investigation of one or more characteristics or a population.
Ex: __________________________________________________________________________
Example: Decide which method of data collection you would use to collect data for
the study.
a) A study of the effect on the taste of popular soda with less carbonation.
o
o
o
o
Experiment
Survey
Simulation
Observational Study
b) A study of how fast a cloud of volcanic ash would spread over a
metropolitan area.
o Experiment
o Survey
o Simulation
o Observational Study
c) A study of how often people wash their hands in public restrooms.
o
o
o
o
Experiment
Survey
Simulation
Observational Study
d) A study of the success of graduates of a large university in finding a job
within one year of graduation.
o
o
o
o
Experiment
Survey
Simulation
Observational Study
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Example: A researcher is interested in the effects of watching videos just before
bed on the quality of sleep. He has decided to test the claim, “Watching 1 hour of
video just before going to bed reduces the number of minutes of REM sleep by more
than 10%.” Which of the following data collection processes would be appropriate?
Select only one answer choice.
A. Choose a random sample of people and ask them how many hours of video they
watched last night and how much REM sleep they had.
B. Choose a random sample of people. Randomly select half of them and have them
watch one hour of video just before going to bed, and then monitor their sleep. Have
the other half not watch any video and monitor their sleep.
C. Choose a random sample of people. On multiple randomly selected nights,
randomly assign each person to either watch one hour of video or not watch video
and monitor their sleep.
D. Choose a random sample of people. On multiple randomly selected nights,
measure the amount of video they watch and monitor their sleep.
Vocabulary
•
Census: Count or measure of an entire population.
•
Sampling: a count or measure of part of a population.
•
Random Sample: one in which every member of the population has a
chance of being selected.
Sampling Techniques:
•
Simple Random Sample: a sample in which every possible member has the
same (equal) chance of being selected.
•
Stratified Sample: Divide a population into groups (strata) and select a
random sample from each group.
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•
Cluster Sample: Divide the population into groups (clusters) and select all
of the members in one or more, but not all, of the clusters.
•
Systematic Sample: Choose a starting value at random. Then choose every
kth member of the population.
•
Convenience Sample: a sample that often leads to biased studies; consists
only of members of the population that are easy to get.
_______________________________________________________________________________
Example: Which method of data collection is being used to collect data for each of
the following studies?
A Study of the health of every lung transplant patient at a hospital.
a) Cluster Sampling
b) Stratified Sampling
c) Census
d) Systematic Sampling
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Questioning college students, as they leave their fraternity and sorority
houses, a researcher asks 358 students about their drinking habits.
a) Systematic
b) Simple Random
c) Stratified
d) Convenience
e) Cluster
To determine her body temperature, Carolyn divides up her day into three
parts: morning, afternoon, and evening. She then measures her body
temperatures at 3 randomly selected times during each part of the day.
a) Systematic
b) Simple Random
c) Stratified
d) Convenience
e) Cluster
You are doing a study to determine the opinion of students at your school
regarding stem cell research. You select a class at random and question each
student in the class.
a) Systematic
b) Simple Random
c) Stratified
d) Convenience
e) Cluster
Example: Determine if the survey question is biased. If the question is biased, then
suggest a better wording.
a) Why does texting while driving increase the risk of a crash?
b) How many times do you exercise in an average week?
_____________________________________________________________________________________________
©2021 Chamberlain University
Statistics
Statistics is largely a science of collecting, organizing, and interpreting data. From this
definition, we get a good idea of what we will be learning in this class. In Chapters 1 and 2,
we will learn about collecting data and how we can use data.
Statistics is an important tool for making a variety of health science decisions. For example,
pharmaceutical companies will use data to see if their drug is improving health. For surgery
decisions, statistics are shown based on proportions of successes or probable outcomes.
Because statistics is used so often, it is important to understand the concepts when entering
the health sciences.
Population Versus Sample
The very basis of statistics is to understand the difference between a population and a sample.
A population is the all, so to speak. If you are talking about all of the students taking an
introductory statistics class, you have a large population. This could include students taking
introductory statistics at Chamberlain University, at other universities in the states, at
universities in other countries, and even some high schools. Usually, the population is a very
large group.
Because of the size of a population, we may want to investigate a smaller subset of that
population. This is our sample. A sample is a more manageable group that represents, or
reflects, the population. For instance, if our population is all students taking an introductory
statistics class, then our sample may be students at Chamberlain taking an introductory
statistics class. While still a large group, it is a subset of the stated population. As a second
example, if we considered all coronary angioplasty patients and studied 100 of them, the 100
would be our sample of the total population of angioplasty patients.
The differences between a sample and a population are important to distinguish. In some
cases, different formulas are used if we are talking about a population or a sample. Further,
sample data are used to make decisions about a population.
Performing a Statistic Study
Every statistical study is performed with the same basic steps.
1. State a goal. You will state what you are interested in studying, which will define the
population of interest.
2. Take a sample. Typically, it would be too time consuming or costly to survey or test every
member of your population, so you will need to decide how to create a manageable subset,
or sample. You will decide the best sampling technique specific to this goal.
3. Collect your data. Now, you need to collect the data. You will also need to decide the best
collection strategy, specific to this goal.
4. Make an inference about the population. This sample data will lead you to make a decision
about your population. In statistics, we make our decisions about a population from our
sample data.
5. Draw a conclusion. Did this sample answer the questions you wanted answered regarding
your original goal? Sometimes, the answer here may be no. If not, then you may need to
refine your goal and start all over.
Understanding the steps of a statistical study will make your task easier. If you do not plan
well, then you may come to the end of your study without the correct data necessary to
make the right decision. Putting the time and thought into the process from the beginning
will lead to better results in the end.
Types of Statistical Studies
Observational: Observe or measure characteristics without influencing the results. An
example would be watching children play to study their interactions.
Experimental: Study the effects of a treatment. An experiment could be used to study a new
cold medicine. People with colds would be divided into two groups: one that take a new
medicine and one group that takes a placebo. The results from the two groups are then
compared using statistics to see if the new medicine is effective.
Design of Experiments
Three types of good design methods for experiments include replication, blinding, and
randomization.
•
•
•
Replication is an experiment that is repeated on more than one individual. Sample sizes
must be large enough to show marked effects of treatments.
Blinding is an experiment in which the subject does not know if he/she is receiving a
treatment or a placebo (a harmless pill or medicine). Blinding is a way to guard against
the placebo effect, which occurs when an untreated person believes there are
improvements, either real or imagined, in his/her symptoms.
Randomization occurs when individual subjects are assigment to different groups through a
random selection process.
Sampling Techniques
There are several basic sampling techniques that you could use. Choosing the correct
technique will depend on your goal.
1. Systematic sampling—Systematic sampling will choose every nth member. A good example
of a systematic sample is patient satisfaction interviews. If a quality assurance program
wants to gain personal insights into patient satisfaction, then it could systematically pick
every 25th patient discharged to make sure that a range of patient characteristics are
included in the study.
2. Convenience sampling—A convenient sample is created just that way—conveniently. If
you are interested in finding out the predominant eye color of coffee drinkers, then where
is the best place to find coffee drinkers? You may stand outside of a Starbucks and survey
everyone’s eye colors. It is convenient to find coffee drinkers at a Starbucks.
3. Cluster sampling—A cluster sample creates clusters from a population, randomly selects
some of those clusters, and then include all the people or things within the selected clusters
as the sample. For example, if you are interested in determining the average income per
household within your state, you may use each of the counties of the state as a cluster. If
you randomly select two or three of those counties and survey the households’ incomes in
those selected counties, you would have a cluster sampling of your state.
4. Stratified sampling—A stratified sample is a defined subgroup of the population. A stratified
sample would include a similar percentage in the sample as represented in the populations.
A familiar example of a stratified sample would be from a hospital unit. If you are interested
in seeing if a particular unit has more satisfaction among the staff, then the strata from your
population would be unit level. If the hospital has 3,000 staff consisting of 30% in surgery,
28% in neonatal, 25% cardiac, and 17% pediatric, you would create a sample with the same
percentage of levels. Your sample may have only 100 staff, but you would want the strata to
have the same percentage of units represented.
Data, Data, Data
As we know already, we need data.
Classifying Data
Data are defined in several different ways. First, you need to decide what type of data you
have; then, you can decide what level of data you have.
Type of data
Qualitative—Data placed in nonnumerical categories
QuaLitative data—’L’ is for letters, or nonnumeric
Quantitative—Numeric data
QuaNtitative data—’N’ is for numbers
Another type of classification is between discrete and continuous
Discrete—A whole number, like how many students in class would be a discrete number
Continuous—A number that can take on any value. To distinguish, ask yourself if a decimal
place makes sense. An example would be students’ heights.
Level of measurements (from lowest to highest)
1. Nominal: Qualitative data—No mathematical application
Names, labels, or categories
Examples: Numbers on a football jersey, models of cars, gender
2. Ordinal: Qualitative data with order—No mathematical application
Qualitative data that is ranked
Examples: First, second, third place; freshman, sophomore, junior, senior
3. Interval: Quantitative—Arbitrary zero
Arbitrary zero does not mean nothing.
Examples: Temperature (in Fahrenheit or Celsius) and year
If the temperature outside is zero, does that mean there is no temperature? No, it is just the
designated zero in that temperature system.
4. Ratio: Quantitative—Zero means nothing
All numbers that are used in mathematical operations
Example: If a salesman made zero sales for the month, he sold nothing. Zero literally means
nothing.
Bias in a Statistical Study
Collecting the right data is very important for the integrity of a research study. If the data
does not represent the intended population, you will create a bias in your results. A biased
sample will bring questions to the effectiveness of the research.
Bias can come in several forms:
•
•
•
Selection Bias: Selecting a sample in a biased way. For example, instead of creating a
stratified sample by units, only administrators were surveyed regarding all staff satisfaction.
As administrators may have a different experience than much of the staff, the data are
biased based on the sampling.
Participation Bias: Voluntary participation. For example, if patient satisfaction surveys are
voluntary, the outcome may be biased and not truly reflect the satisfaction of most patients.
For each of the sampling techniques, try to think of examples that would create bias within
the study.
Percentages and Indices
Percentages are all around from the 25% discount at the store to a 3% pay increase. There is
a basic structure to finding percentages: (ending – beginning) ÷ beginning
So, if a prescription initially cost $50 and was discounted to $40, you could use this formula
to find the percentage of the discount. This is an absolute change of $10. The relative change
is the same as the percentage change. In this example, the beginning price is 50 and the
ending price is 40. Notice that beginning and ending are based on time frame, rather than
which is smaller or bigger. The price used to be $50 and is now $40, so it started at $50 and
ended at $40.
(40 – 50) ÷ 50 = -10 ÷ 50 = -1 ÷ 5, or -20%
So, there was a 20% discount on the original price. The negative in front of the percentage
indicates the value decreased, or went down, from the beginning point to the ending point.
Indices are calculated using percentage changes. Examples of indices are the Consumer Price
Index for inflation or the cardiac index for heart performance. An index has a starting point,
usually set to 100. Then, the other numbers in the index are stated relative to that staring
point. Let’s say that you want to compare the height of a tree from the time you moved to
your home. If you moved in during 2005 and the tree was 4 feet tall, then a height of 4 feet
would be set to an index value of 100. Here is a table of tree heights.
Year
Height of Tree
1995
3 ft
2000
3.8 ft
Index
Year
Height of Tree
Index
2005
4 ft
100
2010
4.6 ft
2015
6.1 ft
To find the index value in other years, take the value in the year of interest and divide it by
the starting point value and multiply the result by 100. To find the index for 1995, the value
in that year was 3 ft and you divide that by the starting point value of 4 ft and then multiply
by 100:
3 ÷ 4 × 100 = 75
So, the index value in 1995 was 75. This same process can be used for the other years in the
table.
Year
Height of Tree
Index
1995
3 ft
75
2000
3.8 ft
95
2005
4 ft
100
2010
6.6 ft
165
2015
8.2 ft
205
You can tell from looking at the index that the tree is about twice as tall as it was when you
moved in.
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